Generation of $3$-connected, planar line graphs

Phoebe Hollowbread-Smith, Riccardo W. Maffucci

Published 2024-04-11Version 1

We classify and construct all line graphs that are $3$-polytopes (planar and $3$-connected). Apart from a few special cases, they are all obtained starting from the medial graphs of cubic (i.e., $3$-regular) $3$-polytopes, by applying two types of graph transformations. This is similar to the generation of other subclasses of $3$-polytopes.